THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 169 
ing. While a stress diagram, as that of Fig. 16, actually obtains in any one frame of such 
a ship, when a shearing force is applied to the adjacent frame, the excessive forces acting on 
the longitudinals above and below the neutral axis will, on the length of a few frame spaces, be 
diverted respectively towards the top and bottom members and bring about a condition more 
and more conforming to the theory of bending. This is due to the elastic strains in the 
longitudinals and can be proved to be in accordance with the Principle of Least Work. It 
conforms to Saint Venant’s Principle, according to which the state of stress and strain set 
up in a bar by a terminal couple is practically independent of the distribution of the forces 
which constitute the couple, and this is true of all parts of the girder except very near the 
region of application of the couple. Hence, although the forces which initiate the bending 
in an airship may not themselves conform to the theory of bending, they will, due to the 
elastic strains in the structure, tend to adjust themselves to that theory. 
As a final argument against the shear method, consider the hypothetical case of a ship 
subject to a pure bending moment produced by simple couples applied to the ends. In that 
case there would be no shearing in the structure, and hence the shear method would fail com- 
pletely to account for the stresses. 
Only by a combination of the bending method with a calculation of the local effects of 
shearing and by superposing the stresses so determined is it possible to obtain a fairly correct 
and complete solution. Where the system of wiring varies abruptly and where it does not con- 
form to the strength of the longitudinals, a solution may be obtained by reckoning the effec- 
tive area of the longitudinals to be proportional to the size of the adjacent wires. This ques- 
tion, however, lies outside of the scope of the present paper, which deals particularly with 
airships of fairly uniform girders and wiring. 
IX. SUMMARY AND CONCLUSIONS. 
1. A wire, so long as it is in tension, will transmit compressive forces as effectively as an 
elastic strut. 
2. A wire may transmit tension and compression without any sensible change in its ten- 
sile stress, as when a free panel is subject to shearing couples which determine a certain ten- 
sion in the shear wire. 
3. When a panel forms part of a larger structure as in an airship, where it is prevented 
from distorting freely and is subject to shearing combined with tension or compression, the 
tension in the shear wire is no longer determined by shearing alone as commonly assumed. 
The tension is then the sum or difference of that due to shearing deflection and that due to 
the direct pull or compression acting at the joints, but the sum of the vertical components of 
the tensions in all the wires in one frame space is equal to the total shear force in that frame 
space. 
